Question: Determine the intercepts of the line. $y-6=4(x+5)$ $y$ -intercept: $\Big($
Explanation: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y-6&=4({0}+5)\\ y-6&=20\\ y&=26\end{aligned}$ So the $y$ -intercept is $\left(0,26\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}-6&=4(x+5)\\ -6&=4x+20\\ -26&=4x\\ -6.5&=x\end{aligned}$ So the $x$ -intercept is $\left(-6.5,0\right)$. In conclusion, The $y$ -intercept is $\left(0,26\right)$. The $x$ -intercept is $\left(-6.5,0\right)$.